What is the smallest integer n for which 25^n 5^12 ?(A) 6(B) 7(C) 8(D) 9(E) 10

Question

What is the smallest integer n for which 25^n > 5^12 ?(A) 6(B) 7(C) 8(D) 9(E) 10

Rakesh Rakesh · Answer

Work with the common base: 25^n=(5^2)^n =5^2nThus we have that 5^2n&gt;5^122n&gt;12n&gt;6&nbsp;n min=7Answer: B.

What is the smallest integer n for which 25^n > 5^12 ?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10